Find the length of a chord which is at a distance of `8 cm` from the centre of a circle of radius `17 cm.`

Options

A. `25 cm`
B. `35 cm`
C. `30 cm`
D. None

Answer

C

Explanation

Let `AB` be a chord of a circle with centre `O` and radius `17 cm.`
Draw `OL` `_|_` `AB`. Join `OA`.
Then , `OL=8cm` and `OA = 17cm`.
From the right `Delta OLA` , we have
`OA^(2)=OL^(2)+AL^(2)`
`implies AL^(2)=OA^(2)-OL^(2)=[(17)^(2)-(8)^(2)]cm^(2)`
`=(17+8)(17-8)cm^(2)=225cm^(2)`
`implies AL=sqrt(225)=15cm`.
Since the perpendicular fromthe centre of a circle to a chord bisects the chord, we have
`AB = 2 xx AL = (2xx15) cm = 30cm`